The origins and the relations of the idea of the dynamic film to the classic results concerning viscosity. How one can pass from one idea to the other, and in the expressions Δu and Δv make the forces tangent and normal to the elements of films appear in the case of movement parallel to a plane.

The introduction and the significance of the curvature φ of rectangular trajectory to the filaments, which comes into the new expressions for Δu and Δv, together with the curvature ψ of the filaments.

The condition of rectangularity between filaments and trajectories gives a relation between ψ and φ and their partial derivatives following these curves. A very simple and new form for the component of the viscous force due to the velocity, with its new notations.

Discussion of results. Experimental study of simple slip—arrangement employed—influence of the proximity of the walls—inadequacy of the classical expressions concerning the forces due to convergence or divergence—plane films with forced uniform motion—schematic picture of actual lubrication in the case of considerable speed of rotation—the zone of crushing (Leslie pressure)—the two zones of viscous acceleration—the surface of zero velocity.

Test of an intrinsic method of rectangular system of coordinates with application to the dynamics of incompressible fluids. Use of the new functions to define a system of curvilinear coordinates by the curves carries to the axes.

The potential of curvature and the factor of torsion. Representation of the expressions γx and γy.

In the first part, the author recalls the principal phenomena concerning the flow of the viscous liquids about an immersed body when the Reynolds numbers are progressively increased. The following factors in order have been studied in the Laboratory of Hydraulics of Toulouse.

1. Curves (C. CAMICHEL AND P. DUPIN);

2. Pressures about a Submerged Body for Small Reynolds Numbers (E. CRAUSSE AND J. BAUBIAC);

3. Similitude of the Limiting Layer for Small Reynolds Numbers (L. ESCANDE AND M. TEISSIE SOLIER);

Soap solutions are unique in that over a wide range of higher concentrations at temperatures from room temperature up to one or two hundred degrees they are doubly refracting and constitute the only easily accessible examples of liquid crystals. Nevertheless, apart from a few photographs published by McBain and the original curious observations of Lehmann on the double conic shape assumed by free drops of ammonium oleate, no study of their liquid crystalline properties has yet appeared, and not even an approximate measurement of their mechanical properties has been recorded in the literature. It is, therefore, of immediate interest to characterize them as being clear, colorless, faintly opalescent, anisotropic liquids whose apparent viscosity is several hundred times greater than that of vaseline at room temperatures. For these reasons we have begun the systematic investigation of their properties.

The earth's magma, a siliceous melt which is believed to underlie the entire solid crust of the earth, is, in all probability, a highly viscous liquid. Wherever molten lava is observed in motion, either in craters of volcanoes (Kilauea, Mauna Loa, Hawaii), or as disastrous flows which descend volcanic mountains (Vesuvius, Mount Aetna, etc.), or in the vicinity of volcanic fissures (Laki, Eldgja rift, Iceland) it behaves like a liquid of appreciable viscosity; the degree of viscosity, however, varies, depending on the proportion of admixed gases and water vapor, and the chemical composition of the lava. Lavas rich in silica are highly viscous (rhyolite, dacite), while those rich in iron and magnesium (basalt, andesite) are more fluid. The viscosity of every lava flow increases until the melt slowly freezes, because of the chilling effect of the surface temperatures on the earth.

The paper of Bingham and Fornwalt showed the need for fluidities of additional pure associated liquids. This paper is intended to supply that need particularly in the group of esters. The substances employed were obtained from the Eastman Kodak Company, but before use they were dehydrated with calcium chloride and distilled, the middle fraction being measured. Viscometer 1–23 and pyenometer 1–29 were used. The data on the fluidities and specific volumes are given in Tables I to XVII. The fluidity curves are nearly linear, and from the curves were read the temperatures required to give a certain desired fluidity, as, for example, 200 rhes. The atomic temperatures of Bingham and Spooner were used to calculate these temperatures, and the ratio of these two values gave the association n. These values are given in Table XVIII.

Experimental investigations of Freundlich, Zocher, and others have shown that birefringence induced by flow in colloids arises from the tendency of nonspherical particles to orientate under the mechanical stresses within the fluid.

At the present stage of the metal‐working industry the treatment of metals by pressure is one of the most important technological processes. Further development of technique will, no doubt, only increase the significance of this process. It must be stated, however, that the working of metals by pressure has as yet no strictly scientific basis. The theory of the mechanics of the plastic deformation of bodies, on which the working of metals by pressure is based, finds itself in the initial phase of its development and is far from being in a state where we can guide ourselves by it directly in our industrial work.